Abstract

The locomotion of bacteria, such as Escherichia coli, is powered by a rotary motor embedded in the cell wall that rotates rigid helical filaments called flagella, connected to a short elastic hook via a universal joint. There have been a few studies to compute the value of the torque of this rotary motor using resistive force theory (Darnton et al., Biophys. J, 2007). However, there is a big discrepancy between the observed experimental value, 1280 pN.nm and that calculated by resistive force theory, 370 pN.nm. In this work, we develop a numerical method based on boundary element method and slender body theory to model a bacterium tethered to a wall. Our model predicts the motor torque to range between 500 to 850 pN.nm depending on the configuration of the bacterium placed next to a solid wall. This shows that hydrodynamics alone cannot explain the discrepancy between the values obtained by more accurate numerical simulations and those observed in experiments. Possible sources of discrepancies include inaccurate measurement of viscosity in which the bacterium resides and presence of additional rigid body friction due to contact of the rotating flagellum with the wall.